text: # Copyright 2005-2008 by Frank Kauff & Cymon J. Cox. All rights reserved.
  #
  # This file is part of the Biopython distribution and governed by your
  # choice of the "Biopython License Agreement" or the "BSD 3-Clause License".
  # Please see the LICENSE file that should have been included as part of this
  # package.
  
  """Tree class to handle phylogenetic trees.
  
  Provides a set of methods to read and write newick-format tree descriptions,
  get information about trees (monphyly of taxon sets, congruence between trees,
  common ancestors,...) and to manipulate trees (re-root trees, split terminal
  nodes).
  """
  
  from __future__ import print_function
  
  import random
  import sys
  from . import Nodes
  
  
  PRECISION_BRANCHLENGTH = 6
  PRECISION_SUPPORT = 6
  NODECOMMENT_START = "[&"
  NODECOMMENT_END = "]"
  
  
  class TreeError(Exception):
      """Provision for the management of Tree exceptions."""
  
      pass
  
  
  class NodeData(object):
      """Store tree-relevant data associated with nodes (e.g. branches or otus)."""
  
      def __init__(self, taxon=None, branchlength=0.0, support=None, comment=None):
          """Initialize the class."""
          self.taxon = taxon
          self.branchlength = branchlength
          self.support = support
          self.comment = comment
  
  
  class Tree(Nodes.Chain):
      """Represent a tree using a chain of nodes with on predecessor (=ancestor) and multiple successors (=subclades)."""
  
      # A newick tree is parsed into nested list and then converted to a node list in two stages
      # mostly due to historical reasons. This could be done in one swoop). Note: parentheses ( ) and
      # colon : are not allowed in taxon names. This is against NEXUS standard, but makes life much
      # easier when parsing trees.
  
      # NOTE: Tree should store its data class in something like self.dataclass=data,
      # so that nodes that are generated have easy access to the data class
      # Some routines use automatically NodeData, this needs to be more concise
  
      def __init__(self, tree=None, weight=1.0, rooted=False, name="", data=NodeData, values_are_support=False, max_support=1.0):
          """Ntree(self,tree)."""
          Nodes.Chain.__init__(self)
          self.dataclass = data
          self.__values_are_support = values_are_support
          self.max_support = max_support
          self.weight = weight
          self.rooted = rooted
          self.name = name
          root = Nodes.Node(data())
          self.root = self.add(root)
          if tree:    # use the tree we have
              # if Tree is called from outside Nexus parser, we need to get rid of linebreaks, etc
              tree = tree.strip().replace("\n", "").replace("\r", "")
              # there's discrepancy whether newick allows semicolons et the end
              tree = tree.rstrip(";")
              subtree_info, base_info = self._parse(tree)
              root.data = self._add_nodedata(root.data, [[], base_info])
              self._add_subtree(parent_id=root.id, tree=subtree_info)
  
      def _parse(self, tree):
          """Parse (a,b,c...)[[[xx]:]yy] into subcomponents and travels down recursively (PRIVATE)."""
          # Remove any leading/trailing white space - want any string starting
          # with " (..." should be recognised as a leaf, "(..."
          tree = tree.strip()
          if tree.count("(") != tree.count(")"):
              raise TreeError("Parentheses do not match in (sub)tree: " + tree)
          if tree.count("(") == 0:  # a leaf
              # check if there's a colon, or a special comment, or both  after the taxon name
              nodecomment = tree.find(NODECOMMENT_START)
              colon = tree.find(":")
              if colon == -1 and nodecomment == -1:  # none
                  return [tree, [None]]
              elif colon == -1 and nodecomment > -1:  # only special comment
                  return [tree[:nodecomment], self._get_values(tree[nodecomment:])]
              elif colon > -1 and nodecomment == -1:  # only numerical values
                  return [tree[:colon], self._get_values(tree[colon + 1:])]
              elif colon < nodecomment:  # taxon name ends at first colon or with special comment
                  return [tree[:colon], self._get_values(tree[colon + 1:])]
              else:
                  return [tree[:nodecomment], self._get_values(tree[nodecomment:])]
          else:
              closing = tree.rfind(")")
              val = self._get_values(tree[closing + 1:])
              if not val:
                  val = [None]
              subtrees = []
              plevel = 0
              prev = 1
              incomment = False
              for p in range(1, closing):
                  if not incomment and tree[p] == "(":
                      plevel += 1
                  elif not incomment and tree[p] == ")":
                      plevel -= 1
                  elif tree[p:].startswith(NODECOMMENT_START):
                      incomment = True
                  elif incomment and tree[p] == NODECOMMENT_END:
                      incomment = False
                  elif not incomment and tree[p] == "," and plevel == 0:
                      subtrees.append(tree[prev:p])
                      prev = p + 1
  
              subtrees.append(tree[prev:closing])
              subclades = [self._parse(subtree) for subtree in subtrees]
              return [subclades, val]
  
      def _add_subtree(self, parent_id=None, tree=None):
          """Add leaf or tree (in newick format) to a parent_id (PRIVATE)."""
          if parent_id is None:
              raise TreeError("Need node_id to connect to.")
          for st in tree:
              nd = self.dataclass()
              nd = self._add_nodedata(nd, st)
              if isinstance(st[0], list):  # it's a subtree
                  sn = Nodes.Node(nd)
                  self.add(sn, parent_id)
                  self._add_subtree(sn.id, st[0])
              else:  # it's a leaf
                  nd.taxon = st[0]
                  leaf = Nodes.Node(nd)
                  self.add(leaf, parent_id)
  
      def _add_nodedata(self, nd, st):
          """Add data to the node parsed from the comments, taxon and support (PRIVATE)."""
          if isinstance(st[1][-1], str) and st[1][-1].startswith(NODECOMMENT_START):
              nd.comment = st[1].pop(-1)
          # if the first element is a string, it's the subtree node taxon
          elif isinstance(st[1][0], str):
              nd.taxon = st[1][0]
              st[1] = st[1][1:]
          if len(st) > 1:
              if len(st[1]) >= 2:  # if there's two values, support comes first. Is that always so?
                  nd.support = st[1][0]
                  if st[1][1] is not None:
                      nd.branchlength = st[1][1]
              elif len(st[1]) == 1:  # otherwise it could be real branchlengths or support as branchlengths
                  if not self.__values_are_support:  # default
                      if st[1][0] is not None:
                          nd.branchlength = st[1][0]
                  else:
                      nd.support = st[1][0]
          return nd
  
      def _get_values(self, text):
          """Extract values (support/branchlength) from xx[:yyy], xx (PRIVATE)."""
          if text == "":
              return None
          nodecomment = None
          if NODECOMMENT_START in text:  # if there's a [&....] comment, cut it out
              nc_start = text.find(NODECOMMENT_START)
              nc_end = text.find(NODECOMMENT_END)
              if nc_end == -1:
                  raise TreeError("Error in tree description: Found %s without matching %s"
                                  % (NODECOMMENT_START, NODECOMMENT_END))
              nodecomment = text[nc_start:nc_end + 1]
              text = text[:nc_start] + text[nc_end + 1:]
  
          # pase out supports and branchlengths, with internal node taxa info
          values = []
          taxonomy = None
          for part in [t.strip() for t in text.split(":")]:
              if part:
                  try:
                      values.append(float(part))
                  except ValueError:
                      assert taxonomy is None, "Two string taxonomies?"
                      taxonomy = part
          if taxonomy:
              values.insert(0, taxonomy)
          if nodecomment:
              values.append(nodecomment)
          return values
  
      def _walk(self, node=None):
          """Return all node_ids downwards from a node (PRIVATE)."""
          if node is None:
              node = self.root
          for n in self.node(node).succ:
              yield n
              for sn in self._walk(n):
                  yield sn
  
      def node(self, node_id):
          """Return the instance of node_id.
  
          node = node(self,node_id)
          """
          if node_id not in self.chain:
              raise TreeError("Unknown node_id: %d" % node_id)
          return self.chain[node_id]
  
      def split(self, parent_id=None, n=2, branchlength=1.0):
          """Speciation: generates n (default two) descendants of a node.
  
          [new ids] = split(self,parent_id=None,n=2,branchlength=1.0):
          """
          if parent_id is None:
              raise TreeError("Missing node_id.")
          ids = []
          parent_data = self.chain[parent_id].data
          for i in range(n):
              node = Nodes.Node()
              if parent_data:
                  node.data = self.dataclass()
                  # each node has taxon and branchlength attribute
                  if parent_data.taxon:
                      node.data.taxon = parent_data.taxon + str(i)
                  node.data.branchlength = branchlength
              ids.append(self.add(node, parent_id))
          return ids
  
      def search_taxon(self, taxon):
          """Return the first matching taxon in self.data.taxon. Not restricted to terminal nodes.
  
          node_id = search_taxon(self,taxon)
  
          """
          for id, node in self.chain.items():
              if node.data.taxon == taxon:
                  return id
          return None
  
      def prune(self, taxon):
          """Prune a terminal taxon from the tree.
  
          id_of_previous_node = prune(self,taxon)
          If taxon is from a bifurcation, the connectiong node will be collapsed
          and its branchlength added to remaining terminal node. This might be no
          longer a meaningful value'
          """
          id = self.search_taxon(taxon)
          if id is None:
              raise TreeError("Taxon not found: %s" % taxon)
          elif id not in self.get_terminals():
              raise TreeError("Not a terminal taxon: %s" % taxon)
          else:
              prev = self.unlink(id)
              self.kill(id)
              if len(self.node(prev).succ) == 1:
                  if prev == self.root:  # we deleted one branch of a bifurcating root, then we have to move the root upwards
                      self.root = self.node(self.root).succ[0]
                      self.node(self.root).branchlength = 0.0
                      self.kill(prev)
                  else:
                      succ = self.node(prev).succ[0]
                      new_bl = self.node(prev).data.branchlength + self.node(succ).data.branchlength
                      self.collapse(prev)
                      self.node(succ).data.branchlength = new_bl
              return prev
  
      def get_taxa(self, node_id=None):
          """Return a list of all otus downwards from a node.
  
          nodes = get_taxa(self,node_id=None)
          """
          if node_id is None:
              node_id = self.root
          if node_id not in self.chain:
              raise TreeError("Unknown node_id: %d." % node_id)
          if self.chain[node_id].succ == []:
              if self.chain[node_id].data:
                  return [self.chain[node_id].data.taxon]
              else:
                  return None
          else:
              list = []
              for succ in self.chain[node_id].succ:
                  list.extend(self.get_taxa(succ))
              return list
  
      def get_terminals(self):
          """Return a list of all terminal nodes."""
          return [i for i in self.all_ids() if self.node(i).succ == []]
  
      def is_terminal(self, node):
          """Return True if node is a terminal node."""
          return self.node(node).succ == []
  
      def is_internal(self, node):
          """Return True if node is an internal node."""
          return len(self.node(node).succ) > 0
  
      def is_preterminal(self, node):
          """Return True if all successors of a node are terminal ones."""
          if self.is_terminal(node):
              return False not in [self.is_terminal(n) for n in self.node(node).succ]
          else:
              return False
  
      def count_terminals(self, node=None):
          """Count the number of terminal nodes that are attached to a node."""
          if node is None:
              node = self.root
          return len([n for n in self._walk(node) if self.is_terminal(n)])
  
      def collapse_genera(self, space_equals_underscore=True):
          """Collapse all subtrees which belong to the same genus.
  
          (i.e share the same first word in their taxon name.)
          """
          while True:
              for n in self._walk():
                  if self.is_terminal(n):
                      continue
                  taxa = self.get_taxa(n)
                  genera = []
                  for t in taxa:
                      if space_equals_underscore:
                          t = t.replace(" ", "_")
                      try:
                          genus = t.split("_", 1)[0]
                      except IndexError:
                          genus = "None"
                      if genus not in genera:
                          genera.append(genus)
                  if len(genera) == 1:
                      self.node(n).data.taxon = genera[0] + " <collapsed>"
                      # now we kill all nodes downstream
                      nodes2kill = [kn for kn in self._walk(node=n)]
                      for kn in nodes2kill:
                          self.kill(kn)
                      self.node(n).succ = []
                      break  # break out of for loop because node list from _walk will be inconsistent
              else:  # for loop exhausted: no genera to collapse left
                  break  # while
  
      def sum_branchlength(self, root=None, node=None):
          """Add up the branchlengths from root (default self.root) to node.
  
          sum = sum_branchlength(self,root=None,node=None)
          """
          if root is None:
              root = self.root
          if node is None:
              raise TreeError("Missing node id.")
          blen = 0.0
          while node is not None and node is not root:
              blen += self.node(node).data.branchlength
              node = self.node(node).prev
          return blen
  
      def set_subtree(self, node):
          """Return subtree as a set of nested sets.
  
          sets = set_subtree(self,node)
          """
          if self.node(node).succ == []:
              return self.node(node).data.taxon
          else:
              try:
                  return frozenset(self.set_subtree(n) for n in self.node(node).succ)
              except Exception:
                  print(node)
                  print(self.node(node).succ)
                  for n in self.node(node).succ:
                      print("%s %s" % (n, self.set_subtree(n)))
                  print([self.set_subtree(n) for n in self.node(node).succ])
                  raise
  
      def is_identical(self, tree2):
          """Compare tree and tree2 for identity.
  
          result = is_identical(self,tree2)
          """
          return self.set_subtree(self.root) == tree2.set_subtree(tree2.root)
  
      def is_compatible(self, tree2, threshold, strict=True):
          """Compare branches with support>threshold for compatibility.
  
          result = is_compatible(self,tree2,threshold)
          """
          # check if both trees have the same set of taxa. strict=True enforces this.
          missing2 = set(self.get_taxa()) - set(tree2.get_taxa())
          missing1 = set(tree2.get_taxa()) - set(self.get_taxa())
          if strict and (missing1 or missing2):
              if missing1:
                  print("Taxon/taxa %s is/are missing in tree %s" % (",".join(missing1), self.name))
              if missing2:
                  print("Taxon/taxa %s is/are missing in tree %s" % (",".join(missing2), tree2.name))
              raise TreeError("Can't compare trees with different taxon compositions.")
          t1 = [(set(self.get_taxa(n)), self.node(n).data.support) for n in self.all_ids() if
                self.node(n).succ and
                (self.node(n).data and self.node(n).data.support and self.node(n).data.support >= threshold)]
          t2 = [(set(tree2.get_taxa(n)), tree2.node(n).data.support) for n in tree2.all_ids() if
                tree2.node(n).succ and
                (tree2.node(n).data and tree2.node(n).data.support and tree2.node(n).data.support >= threshold)]
          conflict = []
          for (st1, sup1) in t1:
              for (st2, sup2) in t2:
                  if not st1.issubset(st2) and not st2.issubset(st1):                     # don't hiccup on upstream nodes
                      intersect, notin1, notin2 = st1 & st2, st2 - st1, st1 - st2                 # all three are non-empty sets
                      # if notin1==missing1 or notin2==missing2  <==> st1.issubset(st2) or st2.issubset(st1) ???
                      if intersect and not (notin1.issubset(missing1) or notin2.issubset(missing2)):         # omit conflicts due to missing taxa
                          conflict.append((st1, sup1, st2, sup2, intersect, notin1, notin2))
          return conflict
  
      def common_ancestor(self, node1, node2):
          """Return the common ancestor that connects two nodes.
  
          node_id = common_ancestor(self,node1,node2)
          """
          l1 = [self.root] + self.trace(self.root, node1)
          l2 = [self.root] + self.trace(self.root, node2)
          return [n for n in l1 if n in l2][-1]
  
      def distance(self, node1, node2):
          """Add and return the sum of the branchlengths between two nodes.
  
          dist = distance(self,node1,node2)
          """
          ca = self.common_ancestor(node1, node2)
          return self.sum_branchlength(ca, node1) + self.sum_branchlength(ca, node2)
  
      def is_monophyletic(self, taxon_list):
          """Return node_id of common ancestor if taxon_list is monophyletic, -1 otherwise.
  
          result = is_monophyletic(self,taxon_list)
          """
          if isinstance(taxon_list, str):
              taxon_set = set(taxon_list)
          else:
              taxon_set = set(taxon_list)
          node_id = self.root
          while True:
              subclade_taxa = set(self.get_taxa(node_id))
              if subclade_taxa == taxon_set:                                        # are we there?
                  return node_id
              else:                                                               # check subnodes
                  for subnode in self.chain[node_id].succ:
                      if set(self.get_taxa(subnode)).issuperset(taxon_set):  # taxon_set is downstream
                          node_id = subnode
                          break   # out of for loop
                  else:
                      return -1   # taxon set was not with successors, for loop exhausted
  
      def is_bifurcating(self, node=None):
          """Return True if tree downstream of node is strictly bifurcating."""
          if node is None:
              node = self.root
          if node == self.root and len(self.node(node).succ) == 3:  # root can be trifurcating, because it has no ancestor
              return self.is_bifurcating(self.node(node).succ[0]) and \
                      self.is_bifurcating(self.node(node).succ[1]) and \
                      self.is_bifurcating(self.node(node).succ[2])
          if len(self.node(node).succ) == 2:
              return self.is_bifurcating(self.node(node).succ[0]) and self.is_bifurcating(self.node(node).succ[1])
          elif len(self.node(node).succ) == 0:
              return True
          else:
              return False
  
      def branchlength2support(self):
          """Move values stored in data.branchlength to data.support, and set branchlength to 0.0.
  
          This is necessary when support has been stored as branchlength (e.g. paup), and has thus
          been read in as branchlength.
          """
          for n in self.chain:
              self.node(n).data.support = self.node(n).data.branchlength
              self.node(n).data.branchlength = 0.0
  
      def convert_absolute_support(self, nrep):
          """Convert absolute support (clade-count) to rel. frequencies.
  
          Some software (e.g. PHYLIP consense) just calculate how often clades appear, instead of
          calculating relative frequencies.
          """
          for n in self._walk():
              if self.node(n).data.support:
                  self.node(n).data.support /= float(nrep)
  
      def has_support(self, node=None):
          """Return True if any of the nodes has data.support != None."""
          for n in self._walk(node):
              if self.node(n).data.support:
                  return True
          else:
              return False
  
      def randomize(self, ntax=None, taxon_list=None, branchlength=1.0, branchlength_sd=None, bifurcate=True):
          """Generate a random tree with ntax taxa and/or taxa from taxlabels.
  
          new_tree = randomize(self,ntax=None,taxon_list=None,branchlength=1.0,branchlength_sd=None,bifurcate=True)
          Trees are bifurcating by default. (Polytomies not yet supported).
          """
          if not ntax and taxon_list:
              ntax = len(taxon_list)
          elif not taxon_list and ntax:
              taxon_list = ["taxon" + str(i + 1) for i in range(ntax)]
          elif not ntax and not taxon_list:
              raise TreeError("Either numer of taxa or list of taxa must be specified.")
          elif ntax != len(taxon_list):
              raise TreeError("Length of taxon list must correspond to ntax.")
          # initiate self with empty root
          self.__init__()
          terminals = self.get_terminals()
          # bifurcate randomly at terminal nodes until ntax is reached
          while len(terminals) < ntax:
              newsplit = random.choice(terminals)
              new_terminals = self.split(parent_id=newsplit, branchlength=branchlength)
              # if desired, give some variation to the branch length
              if branchlength_sd:
                  for nt in new_terminals:
                      bl = random.gauss(branchlength, branchlength_sd)
                      if bl < 0:
                          bl = 0
                      self.node(nt).data.branchlength = bl
              terminals.extend(new_terminals)
              terminals.remove(newsplit)
          # distribute taxon labels randomly
          random.shuffle(taxon_list)
          for (node, name) in zip(terminals, taxon_list):
              self.node(node).data.taxon = name
  
      def display(self):
          """Quick and dirty lists of all nodes."""
          table = [("#", "taxon", "prev", "succ", "brlen", "blen (sum)", "support", "comment")]
          # Sort this to be consistent across CPython, Jython, etc
          for i in sorted(self.all_ids()):
              n = self.node(i)
              if not n.data:
                  table.append((str(i), "-", str(n.prev), str(n.succ), "-", "-", "-", "-"))
              else:
                  tx = n.data.taxon
                  if not tx:
                      tx = "-"
                  blength = "%0.2f" % n.data.branchlength
                  if blength is None:
                      blength = "-"
                      sum_blength = "-"
                  else:
                      sum_blength = "%0.2f" % self.sum_branchlength(node=i)
                  support = n.data.support
                  if support is None:
                      support = "-"
                  else:
                      support = "%0.2f" % support
                  comment = n.data.comment
                  if comment is None:
                      comment = "-"
                  table.append((str(i), tx, str(n.prev), str(n.succ),
                               blength, sum_blength, support, comment))
          print("\n".join("%3s %32s %15s %15s %8s %10s %8s %20s" % l for l in table))
          print("\nRoot:  %s" % self.root)
  
      def to_string(self, support_as_branchlengths=False,
                    branchlengths_only=False, plain=True, plain_newick=False,
                    ladderize=None, ignore_comments=True):
          """Return a paup compatible tree line."""
          # if there's a conflict in the arguments, we override plain=True
          if support_as_branchlengths or branchlengths_only:
              plain = False
          self.support_as_branchlengths = support_as_branchlengths
          self.branchlengths_only = branchlengths_only
          self.ignore_comments = ignore_comments
          self.plain = plain
  
          def make_info_string(data, terminal=False):
              """Create nicely formatted support/branchlengths."""
              # CHECK FORMATTING
              if self.plain:  # plain tree only. That's easy.
                  info_string = ""
              elif self.support_as_branchlengths:  # support as branchlengths (eg. PAUP), ignore actual branchlengths
                  if terminal:    # terminal branches have 100% support
                      info_string = ":%1.2f" % self.max_support
                  elif data.support:
                      info_string = ":%1.2f" % (data.support)
                  else:
                      info_string = ":0.00"
              elif self.branchlengths_only:  # write only branchlengths, ignore support
                  info_string = ":%1.5f" % (data.branchlength)
              else:   # write suport and branchlengths (e.g. .con tree of mrbayes)
                  if terminal:
                      info_string = ":%1.5f" % (data.branchlength)
                  else:
                      if data.branchlength is not None and data.support is not None:  # we have blen and suppport
                          info_string = "%1.2f:%1.5f" % (data.support, data.branchlength)
                      elif data.branchlength is not None:                             # we have only blen
                          info_string = "0.00000:%1.5f" % (data.branchlength)
                      elif data.support is not None:                                  # we have only support
                          info_string = "%1.2f:0.00000" % (data.support)
                      else:
                          info_string = "0.00:0.00000"
              if not ignore_comments and hasattr(data, "nodecomment"):
                  info_string = str(data.nodecomment) + info_string
              return info_string
  
          def ladderize_nodes(nodes, ladderize=None):
              """Sort node numbers according to the number of terminal nodes."""
              if ladderize in ["left", "LEFT", "right", "RIGHT"]:
                  succnode_terminals = sorted((self.count_terminals(node=n), n) for n in nodes)
                  if (ladderize == "right" or ladderize == "RIGHT"):
                      succnode_terminals.reverse()
                  if succnode_terminals:
                      succnodes = zip(*succnode_terminals)[1]
                  else:
                      succnodes = []
              else:
                  succnodes = nodes
              return succnodes
  
          def newickize(node, ladderize=None):
              """Convert a node tree to a newick tree recursively."""
              if not self.node(node).succ:    # terminal
                  return self.node(node).data.taxon + make_info_string(self.node(node).data, terminal=True)
              else:
                  succnodes = ladderize_nodes(self.node(node).succ, ladderize=ladderize)
                  subtrees = [newickize(sn, ladderize=ladderize) for sn in succnodes]
                  return "(%s)%s" % (",".join(subtrees), make_info_string(self.node(node).data))
  
          treeline = ["tree"]
          if self.name:
              treeline.append(self.name)
          else:
              treeline.append("a_tree")
          treeline.append("=")
          if self.weight != 1:
              treeline.append("[&W%s]" % str(round(float(self.weight), 3)))
          if self.rooted:
              treeline.append("[&R]")
          succnodes = ladderize_nodes(self.node(self.root).succ)
          subtrees = [newickize(sn, ladderize=ladderize) for sn in succnodes]
          treeline.append("(%s)" % ",".join(subtrees))
          if plain_newick:
              return treeline[-1]
          else:
              return " ".join(treeline) + ";"
  
      def __str__(self):
          """Short version of to_string(), gives plain tree."""
          return self.to_string(plain=True)
  
      def unroot(self):
          """Define a unrooted Tree structure, using data of a rooted Tree."""
          # travel down the rooted tree structure and save all branches and the nodes they connect
  
          def _get_branches(node):
              branches = []
              for b in self.node(node).succ:
                  branches.append([node, b, self.node(b).data.branchlength, self.node(b).data.support])
                  branches.extend(_get_branches(b))
              return branches
  
          self.unrooted = _get_branches(self.root)
          # if root is bifurcating, then it is eliminated
          if len(self.node(self.root).succ) == 2:
              # find the two branches that connect to root
              rootbranches = [b for b in self.unrooted if self.root in b[:2]]
              b1 = self.unrooted.pop(self.unrooted.index(rootbranches[0]))
              b2 = self.unrooted.pop(self.unrooted.index(rootbranches[1]))
              # Connect them two each other. If both have support, it should be identical (or one set to None?).
              # If both have branchlengths, they will be added
              newbranch = [b1[1], b2[1], b1[2] + b2[2]]
              if b1[3] is None:
                  newbranch.append(b2[3])  # either None (both rootbranches are unsupported) or some support
              elif b2[3] is None:
                  newbranch.append(b1[3])  # dito
              elif b1[3] == b2[3]:
                  newbranch.append(b1[3])  # identical support
              elif b1[3] == 0 or b2[3] == 0:
                  newbranch.append(b1[3] + b2[3])  # one is 0, take the other
              else:
                  raise TreeError("Support mismatch in bifurcating root: %f, %f"
                                  % (float(b1[3]), float(b2[3])))
              self.unrooted.append(newbranch)
  
      def root_with_outgroup(self, outgroup=None):
          """Define a tree's root with a reference group outgroup."""
          def _connect_subtree(parent, child):
              """Attach subtree starting with node child to parent (PRIVATE)."""
              for i, branch in enumerate(self.unrooted):
                  if parent in branch[:2] and child in branch[:2]:
                      branch = self.unrooted.pop(i)
                      break
              else:
                  raise TreeError("Unable to connect nodes for rooting: nodes %d and %d are not connected"
                                  % (parent, child))
              self.link(parent, child)
              self.node(child).data.branchlength = branch[2]
              self.node(child).data.support = branch[3]
              # now check if there are more branches connected to the child, and if so, connect them
              child_branches = [b for b in self.unrooted if child in b[:2]]
              for b in child_branches:
                  if child == b[0]:
                      succ = b[1]
                  else:
                      succ = b[0]
                  _connect_subtree(child, succ)
  
          # check the outgroup we're supposed to root with
          if outgroup is None:
              return self.root
          outgroup_node = self.is_monophyletic(outgroup)
          if outgroup_node == -1:
              return -1
          # if tree is already rooted with outgroup on a bifurcating root,
          # or the outgroup includes all taxa on the tree, then we're fine
          if (len(self.node(self.root).succ) == 2 and outgroup_node in self.node(self.root).succ) or outgroup_node == self.root:
              return self.root
  
          self.unroot()
          # now we find the branch that connects outgroup and ingroup
          # print(self.node(outgroup_node).prev)
          for i, b in enumerate(self.unrooted):
              if outgroup_node in b[:2] and self.node(outgroup_node).prev in b[:2]:
                  root_branch = self.unrooted.pop(i)
                  break
          else:
              raise TreeError("Unrooted and rooted Tree do not match")
          if outgroup_node == root_branch[1]:
              ingroup_node = root_branch[0]
          else:
              ingroup_node = root_branch[1]
          # now we destroy the old tree structure, but keep node data. Nodes will be reconnected according to new outgroup
          for n in self.all_ids():
              self.node(n).prev = None
              self.node(n).succ = []
          # now we just add both subtrees (outgroup and ingroup) branch for branch
          root = Nodes.Node(data=NodeData())            # new root
          self.add(root)                              # add to tree description
          self.root = root.id                           # set as root
          self.unrooted.append([root.id, ingroup_node, root_branch[2], root_branch[3]])  # add branch to ingroup to unrooted tree
          self.unrooted.append([root.id, outgroup_node, 0.0, 0.0])   # add branch to outgroup to unrooted tree
          _connect_subtree(root.id, ingroup_node)      # add ingroup
          _connect_subtree(root.id, outgroup_node)     # add outgroup
          # if theres still a lonely node in self.chain, then it's the old root, and we delete it
          oldroot = [i for i in self.all_ids() if self.node(i).prev is None and i != self.root]
          if len(oldroot) > 1:
              raise TreeError("Isolated nodes in tree description: %s"
                              % ",".join(oldroot))
          elif len(oldroot) == 1:
              self.kill(oldroot[0])
          return self.root
  
      def merge_with_support(self, bstrees=None, constree=None, threshold=0.5, outgroup=None):
          """Merge clade support (from consensus or list of bootstrap-trees) with phylogeny.
  
          tree=merge_bootstrap(phylo,bs_tree=<list_of_trees>)
          or
          tree=merge_bootstrap(phylo,consree=consensus_tree with clade support)
          """
          if bstrees and constree:
              raise TreeError("Specify either list of bootstrap trees or consensus tree, not both")
          if not (bstrees or constree):
              raise TreeError("Specify either list of bootstrap trees or consensus tree.")
          # no outgroup specified: use the smallest clade of the root
          if outgroup is None:
              try:
                  succnodes = self.node(self.root).succ
                  smallest = min((len(self.get_taxa(n)), n) for n in succnodes)
                  outgroup = self.get_taxa(smallest[1])
              except Exception:
                  raise TreeError("Error determining outgroup.")
          else:  # root with user specified outgroup
              self.root_with_outgroup(outgroup)
  
          if bstrees:  # calculate consensus
              constree = consensus(bstrees, threshold=threshold, outgroup=outgroup)
          else:
              if not constree.has_support():
                  constree.branchlength2support()
              constree.root_with_outgroup(outgroup)
          # now we travel all nodes, and add support from consensus, if the clade is present in both
          for pnode in self._walk():
              cnode = constree.is_monophyletic(self.get_taxa(pnode))
              if cnode > -1:
                  self.node(pnode).data.support = constree.node(cnode).data.support
  
  
  def consensus(trees, threshold=0.5, outgroup=None):
      """Compute a majority rule consensus tree of all clades with relative frequency>=threshold from a list of trees."""
      total = len(trees)
      if total == 0:
          return None
      # shouldn't we make sure that it's NodeData or subclass??
      dataclass = trees[0].dataclass
      max_support = trees[0].max_support
      clades = {}
      # countclades={}
      alltaxa = set(trees[0].get_taxa())
      # calculate calde frequencies
      for t in trees:
          if alltaxa != set(t.get_taxa()):
              raise TreeError("Trees for consensus must contain the same taxa")
          t.root_with_outgroup(outgroup=outgroup)
          for st_node in t._walk(t.root):
              subclade_taxa = sorted(t.get_taxa(st_node))
              subclade_taxa = str(subclade_taxa)  # lists are not hashable
              if subclade_taxa in clades:
                  clades[subclade_taxa] += float(t.weight) / total
              else:
                  clades[subclade_taxa] = float(t.weight) / total
              # if subclade_taxa in countclades:
              #    countclades[subclade_taxa]+=t.weight
              # else:
              #    countclades[subclade_taxa]=t.weight
      # weed out clades below threshold
      delclades = [c for c, p in clades.items() if round(p, 3) < threshold]  # round can be necessary
      for c in delclades:
          del clades[c]
      # create a tree with a root node
      consensus = Tree(name="consensus_%2.1f" % float(threshold), data=dataclass)
      # each clade needs a node in the new tree, add them as isolated nodes
      for c, s in clades.items():
          node = Nodes.Node(data=dataclass())
          node.data.support = s
          node.data.taxon = set(eval(c))
          consensus.add(node)
      # set root node data
      consensus.node(consensus.root).data.support = None
      consensus.node(consensus.root).data.taxon = alltaxa
      # we sort the nodes by no. of taxa in the clade, so root will be the last
      consensus_ids = consensus.all_ids()
      consensus_ids.sort(key=lambda x: len(consensus.node(x).data.taxon))
      # now we just have to hook each node to the next smallest node that includes all taxa of the current
      for i, current in enumerate(consensus_ids[:-1]):  # skip the last one which is the root
          # print('----')
          # print('current: %s' % consensus.node(current).data.taxon)
          # search remaining nodes
          for parent in consensus_ids[i + 1:]:
              # print('parent: %s' % consensus.node(parent).data.taxon)
              if consensus.node(parent).data.taxon.issuperset(consensus.node(current).data.taxon):
                  break
          else:
              sys.exit("corrupt tree structure?")
          # internal nodes don't have taxa
          if len(consensus.node(current).data.taxon) == 1:
              consensus.node(current).data.taxon = consensus.node(current).data.taxon.pop()
              # reset the support for terminal nodes to maximum
              # consensus.node(current).data.support=max_support
          else:
              consensus.node(current).data.taxon = None
          consensus.link(parent, current)
      # eliminate root taxon name
      consensus.node(consensus_ids[-1]).data.taxon = None
      if alltaxa != set(consensus.get_taxa()):
          raise TreeError("FATAL ERROR: consensus tree is corrupt")
      return consensus
  